NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2

# NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2

## NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2 are the part of NCERT Solutions for Class 7 Maths. Here you can find the NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.2.

### Ex 5.2 Class 7 Maths Question 1.

(i) If a || b, then
1 = 5
(ii) If
4 = 6, then a || b
(iii) If
4 + 5 = 180°, then a || b

Solution:
(i) We have a || b
1 = 5

Property used: If two lines are parallel and cut by a transversal, then the pairs of corresponding angles are equal.

(ii) We have 4 = 6
a || b

Property used: If a pair of alternate angles are equal, then the lines are parallel.

(iii) We have 4 + 5 = 180°
a || b

Property used: If the sum of the co-interior angles is 180°, then the lines are parallel.

### Ex 5.2 Class 7 Maths Question 2.

(i) the pairs of corresponding angles.
(ii) the pairs of alternate interior angles.
(iii) the pairs of interior angles on the same side of the transversal.

Solution:
(i) The pairs of corresponding angles are: 1 and 5, 2 and 6, 4 and 8, 3 and 7.
(ii) The pairs of alternate interior angles are:
2 and 8, 3 and 5.
(iii) The pairs of interior angles on the same side of the transversal are:
2 and 5, 3 and 8.

### Ex 5.2 Class 7 Maths Question 3.

In the given figure, p || q. Find the unknown angles.

Solution:
e + 125° = 180°         (Linear pair of angles)
e = 180° – 125° = 55°
e = f                         (Vertically opposite angles)
f = 55°
a = f = 55°            (Alternate interior angles)
c = a = 55°            (Vertically opposite angles)
d = 125°                  (Corresponding angles)
b = d = 125°         (Vertically opposite angles)
Thus,
a = 55°, b = 125°, c = 55°, d = 125°, e = 55°, f = 55°.

### Ex 5.2 Class 7 Maths Question 4.

Find the value of x in each of the following figures, if l || m.

Solution:
(i) Let the vertically opposite angle of 110° be y.
y = 110°             (Vertically opposite angles)
x + y = 180°     (Sum of interior angle on the same side of transversal)
x + 110° = 180° .
x = 180° – 110° = 70°
Thus, x = 70°
(ii)
x = 100°        (Pair of corresponding angles)

### Ex 5.2 Class 7 Maths Question 5.

In the given figure, the arms of two angles are parallel. If ABC = 70°, then find
(i)
DGC
(ii)
DEF

Solution:
Given: AB || DE and BC || EF
ABC = 70°
(i)
DGC = ABC      (Pair of corresponding angles)
DGC = 70°
(ii)
DEF = DGC
DEF = 70°                (Pair of corresponding angles)

### Ex 5.2 Class 7 Maths Question 6.

In the given figure below, decide whether l is parallel to m.
Solution:
(i) The sum of the interior angles on the same side of transversal
= 126° + 44° = 170° ≠ 180°
l is not parallel to m.

(ii) Let the angle opposite to 75° be x.
x = 75°               (Vertically opposite angles)
The sum of the interior angles on the same side of transversal
= x + 75° = 75° + 75° = 150° ≠ 180°
l is not parallel to m.

(iii) Let the angle opposite to 57° be y.
y = 57°          (Vertically opposite angles)
The sum of the interior angles on the same side of transversal
= 57° + 123° = 180°
l is parallel to m.

(iv) Let the angle opposite to 72° be z.
z = 70°             (Vertically opposite angles)
The sum of the interior angles on the same side of transversal
= z + 98° = 72° + 98° = 170° ≠ 180°
l is not parallel to m.

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